Operator Methods in Quantum Mechanics

Name: Operator Methods in Quantum Mechanics
Price: 18.25 USD
Availability: InStock
ISBN: 9780486425474

ISBN-10: 0486425479

ISBN-13: 9780486425474

Edition: 2002

Authors: Martin Schechter

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Description:

This advanced undergraduate and graduate level text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics.

Book details

List price: $18.95
Copyright year: 2002
Publisher: Dover Publications, Incorporated
Publication date: 2/3/2003
Binding: Hardcover
Pages: 352
Size: 4.75" wide x 8.50" long x 0.75" tall
Weight: 0.748
Language: English



Preface


Acknowledgments


A Message to the Reader


List of Symbols



One-Dimensional Motion



Position



Mathematical Expectation



Momentum



Energy



Observables



Operators



Functions of Observables



Self-Adjoint Operators



Hilbert Space



The Spectral Theorem


Exercises



The Spectrum



The Resolvent



Finding the Spectrum



The Position Operator



The Momentum Operator



The Energy Operator



The Potential



A Class of Functions



The Spectrum of H


Exercises



The Essential Spectrum



An Example



A Calculation



Finding the Eigenvalues



The Domain of H



Back to Hilbert Space



Compact Operators



Relative Compactness



Proof of Theorem 3.7.5


Exercises



The Negative Eigenvalues



The Possibilities



Forms Extensions



The Remaining Proofs



Negative Eigenvalues



Existence of Bound States



Existence of Infinitely Many Bound States



Existence of Only a Finite Number of Bound States



Another Criterion


Exercises



Estimating the Spectrum



Introduction



Some Crucial Lemmas



A Lower Bound for the Spectrum



Lower Bounds for the Essential Spectrum



An Inequality



Bilinear Forms



Intervals Containing the Essential Spectrum



Coincidence of the Essential Spectrum with an Interval



The Harmonic Oscillator



The Morse Potential


Exercises



Scattering Theory



Time Dependence



Scattering States



Properties of the Wave Operators



The Domains of the Wave Operators



Local Singularities


Exercises



Long-Range Potentials



The Coulomb Potential



Some Examples



The Estimates



The Derivatives of V(x)



The Relationship Between X[subscript t] and V(x)



An Identity



The Reduction



Mollifiers


Exercises



Time-Independent Theory



The Resolvent Method



The Theory



A Simple Criterion



The Application


Exercises



Completeness



Definition



The Abstract Theory



Some Identities



Another Form



The Unperturbed Resolvent Operator



The Perturbed Operator



Compact Operators



Analytic Dependence



Projections



An Analytic Function Theorem



The Combined Results



Absolute Continuity



The Intertwining Relations



The Application


Exercises



Strong Completeness



The More Difficult Problem



The Abstract Theory



The Technique



Verification for the Hamiltonian



An Extension



The Principle of Limiting Absorption


Exercises



Oscillating Potentials



A Surprise



The Hamiltonian



The Estimates



A Variation



Examples


Exercises



Eigenfunction Expansions



The Usefulness



The Problem



Operators on L[superscript p]



Weighted L[superscript p]-Spaces



Extended Resolvents



The Formulas



Some Consequences



Summary


Exercises



Restricted Particles



A Particle Between Walls



The Energy Levels



Compact Resolvents



One Opaque Wall



Scattering on a Half-Line



The Spectral Resolution for the Free Particle on a Half-Line


Exercises



Hard-Core Potentials



Local Absorption



The Modified Hamiltonian



The Resolvent Operator for H[subscript 1]



The Wave Operators W[subscript plus or minus] (H[subscript 1] H[subscript 0])



Propagation



Proof of Theorem 14.5.1



Completeness of the Wave Operators W[subscript plus or minus], (H[subscript 1] H[subscript 0])



The Wave Operators W[subscript plus or minus] (H, H[subscript 1])



A Regularity Theorem



A Family of Spaces


Exercises



The Invariance Principle



Introduction



A Simple Result



The Estimates



An Extension



Another Form


Exercises



Trace Class Operators



The Abstract Theorem



Some Consequences



Hilbert--Schmidt Operators



Verification for the Hamiltonian


Exercises



The Fourier Transform


Exercises A



Hilbert Space


Exercises B



Holder's Inequality and Banach Space


Bibliography


Index